The jet function for the factorized cross section e[superscript +]e[superscript -] into dijets is given as a function of the jet invariant mass s and with a generic jet algorithm at O(αs). We demonstrate the results using the Sterman-Weinberg algorithm and show that the jet function is independent of the energy fraction β of the soft radiation. The anomalous dimension has the same form with and without the cone half-angle δ. The dependence of the finite part of the jet function on the cone angle is given.